Question: Solve for $x$ and $y$ using substitution. ${-2x+3y = 9}$ ${y = 2x+7}$
Solution: Since $y$ has already been solved for, substitute $2x+7$ for $y$ in the first equation. ${-2x + 3}{(2x+7)}{= 9}$ Simplify and solve for $x$ $-2x+6x + 21 = 9$ $4x+21 = 9$ $4x+21{-21} = 9{-21}$ $4x = -12$ $\dfrac{4x}{{4}} = \dfrac{-12}{{4}}$ ${x = -3}$ Now that you know ${x = -3}$ , plug it back into $\thinspace {y = 2x+7}\thinspace$ to find $y$ ${y = 2}{(-3)}{ + 7}$ $y = -6 + 7$ $y = 1$ You can also plug ${x = -3}$ into $\thinspace {-2x+3y = 9}\thinspace$ and get the same answer for $y$ : ${-2}{(-3)}{ + 3y = 9}$ ${y = 1}$